Arnold cat map

The Arnold Cat map is an area-preserving map on the two-dimensional torus defined by

$$\begin{pmatrix} x' \\ y' \end{pmatrix} = \begin{pmatrix} 2 & 1 \\ 1 & 1 \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} \mod 1 \;.$$ It was introduced by Vladimir Arnold and he used a sketch of a cat to illustrate the chaotic properties of this map. It is an example of an Anosov diffeomorphism.

References

Arnold, V. I. and A. Avez (1968). Ergodic Problems of Classical Mechanics. New York, Benjamin.

See Also

Dynamical Systems, Mapping, Anosov Diffeomorphism